# Lectures on Generating Functions

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*S. K. Lando*

This book introduces readers to the language of generating functions,
which nowadays, is the main language of enumerative combinatorics. The
book starts with definitions, simple properties, and numerous examples
of generating functions. It then discusses topics such as formal
grammars, generating functions in several variables, partitions and
decompositions, and the exclusion-inclusion principle. In the final
chapter, the author describes applications to enumeration of trees,
plane graphs, and graphs embedded in two-dimensional surfaces.

Throughout the book, the author motivates readers by giving interesting
examples rather than general theories. It contains numerous exercises to
help students master the material. The only prerequisite is a standard
calculus course. The book is an excellent text for a one-semester
undergraduate course in combinatorics.

#### Readership

Advanced undergraduates, graduate students, and research mathematicians interested in modern methods of combinatorics.

#### Reviews & Endorsements

A crisp and sophisticated text … More examples than general theory. Covers standard material, but digs deeper … An enjoyable read for professionals.

-- MAA Monthly

(This book) is driven by very, very interesting problems and examples.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## Lectures on Generating Functions

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface to the English Edition xi12 free
- Preface xiii14 free
- Formal power series and generating functions. Operations with formal power series. Elementary generating functions 118 free
- Generating functions for well-known sequences 1734
- Unambiguous formal grammars. The Lagrange theorem 3552
- Analytic properties of functions represented as power series and their asymptotics of their coefficients 4764
- Generating functions of several variables 5976
- Partitions and decompositions 87104
- Dirichlet generating functions and the inclusion-exclusion principle 101118
- Enumeration of embedded graphs 113130
- Final and bibliographical remarks 143160
- Bibliography 145162
- Index 147164 free
- Back Cover Back Cover1170